Method and apparatus of encoding and decoding data using low density parity check code in a wireless communication system

ABSTRACT

A method of encoding data using low density parity check (LDPC) code defined by a m×n parity check matrix is disclosed. More specifically, the method includes encoding input source data using the parity check matrix, wherein the parity check matrix comprises a plurality of z×z sub-matrices of which row weights and column weights are ‘0’ or ‘1’.

This application claims the benefits of the following Korean ApplicationNumbers which are hereby incorporated by reference. They are:

-   -   Korean Application No. P2004-47898, filed on Jun. 24, 2004;    -   Korean Application No. P2004-48454, filed on Jun. 25, 2004;    -   Korean Application No. P2004-85512, filed on Oct. 25, 2004;    -   Korean Application No. P2004-87361, filed on Oct. 29, 2004;    -   Korean Application No. P2004-87938, filed on Nov. 1, 2004;    -   Korean Application No. P2004-88807, filed on Nov. 3, 2004;    -   Korean Application No. P2004-109624, filed on Dec. 1, 2004;    -   Korean Application No. P2004-110678, filed on Dec. 22, 2004;    -   Korean Application No. P2004-111525, filed on Dec. 23, 2004;    -   Korean Application No. P2004-117136, filed on Dec. 30, 2004;    -   Korean Application No. P2005-00046, filed on Jan. 3, 2005;    -   Korean Application No. P2005-00244, filed on Jan. 3, 2005; and    -   Korean Application No. P2005-03296, filed on Jan. 13, 2005.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of encoding and decoding in awireless communication system, and more particularly, to a method andapparatus of encoding and decoding data using low density parity check(LDPC) code in a wireless communication system. Although the presentinvention is suitable for a wide scope of applications, it isparticularly suitable for simplifying complex operations and efficientlyusing the memory space.

2. Discussion of the Related Art

Generally, encoding signifies a process in which data is coded at atransmitting end to enable a receiving end to compensate for errorsoccurring from signal distortion and signal loss during datatransmission through the air interface and recover the original data.Decoding is a process in which encoded data from the transmitting end isrecovered to its original data at the receiving end.

A method of encoding using Low Density Parity Check (LDPC) code isknown. The LDPC code is a type of error-correcting code invented byRobert Gallager in his PhD thesis in 1962. More specifically, the paritycheck matrix H, the elements of which are mostly comprised of ‘0’s, is alow density linear block code. The LDPC codes were largely forgottenwhen first introduced due to the high complexity computations, but werereinvented in 1995 and proven effective. Research of the LDPC codes isunder way (Reference: Robert G. Gallager, “Low-Density Parity-CheckCodes”, The MIT Press, Sep. 15, 1963. [2] D. J. C. Mackay, Gooderror-correcting codes based on very sparse matrices, IEEE Trans.Inform. Theory, IT-45, pp. 399-431(1999)).

The parity check matrix of the LPDC code has very few 1's in each rowand column. As a result, even in a large block, decoding is possiblethrough a repetitive decoding procedure and, if the size of the blockbecomes very large, the LPDC code nearly satisfies Shannon's channelcapacity limit as in turbo coding.

The LPDC code can be defined by a (n-k)×n parity check matrix H, wherein‘n’ denotes the size of codeword after encoding process and ‘k’ denotesthe size of data bits before encoding process. The generator matrix Gcan be derived from the following equation.H×G=0  [Equation 1]

With respect to encoding and decoding using the LDPC code, thetransmitting end uses the parity check matrix H and the generator matrixG to encode data according to Equation 2.c=G×u  [Equation 2]

In Equation 2, the symbol ‘c’ refers to codeword and ‘u’ refers to dataframe.

Recently, a method of encoding data using only the parity check matrix Hand not the generator matrix G is being used. With respect to theencoding method using the LDPC code, the parity check matrix H can beconsidered to be the most important factor. Because the size of theparity check matrix H is approximately 1000×2000 or larger in practicalcommunication system, the process of encoding and decoding requires manycalculations, complex expressions, and large storage space.

After the parity check matrix H is generated, the input source data isencoded using the generated parity check matrix H.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to a method and apparatusof encoding and decoding data using low density parity check in awireless communication system that substantially obviates one or moreproblems due to limitations and disadvantages of the related art.

An object of the present invention is to provide a method for encodingdata using LDPC code.

Another object of the present invention is to provide an apparatus forencoding data using LDPC code.

Additional advantages, objects, and features of the invention will beset forth in part in the description which follows and in part willbecome apparent to those having ordinary skill in the art uponexamination of the following or may be learned from practice of theinvention. The objectives and other advantages of the invention may berealized and attained by the structure particularly pointed out in thewritten description and claims hereof as well as the appended drawings.

To achieve these objects and other advantages and in accordance with thepurpose of the invention, as embodied and broadly described herein. Amethod of encoding or decoding data using low density parity check(LDPC) code, the method comprising using a parity matrix comprising aplurality of z-by-z zero sub matrices and a plurality of z-by-zpermutation sub matrices. Wherein a plurality of z×z permutationsub-matrices of which row weights and column weights are ‘0’ or ‘1’.

In one aspect of the present invention, a method of encoding data usinglow density parity check (LDPC) code is provided, the method comprisingproviding a permutation matrix, a zero matrix and a base matrixgenerating a parity matrix by expanding the base matrix using thepermutation matrix, zero matrix; and using the parity matrix to encodedata to be transmitted.

In another aspect of the present invention, a method of encoding inputsource data using low density parity check (LDPC) code is defined by abase matrix having each element possesses permutation information foridentifying a permutation matrix formed by shifting each row of the basepermutation matrix a certain number of row intervals in the samedirection. In this method, each element of the base matrix is a 96×96permutation matrix and the base matrix is $\begin{bmatrix}2 & {- 1} & 19 & {- 1} & 47 & {- 1} & 48 & {- 1} & 36 & {- 1} & 82 & {- 1} & 47 & {- 1} & 15 & {- 1} & X & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 69 & {- 1} & 88 & {- 1} & 33 & {- 1} & 3 & {- 1} & 16 & {- 1} & 37 & {- 1} & 40 & {- 1} & 48 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\10 & {- 1} & 86 & {- 1} & 62 & {- 1} & 28 & {- 1} & 85 & {- 1} & 16 & {- 1} & 34 & {- 1} & 73 & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 28 & {- 1} & 32 & {- 1} & 81 & {- 1} & 27 & {- 1} & 88 & {- 1} & 5 & {- 1} & 56 & {- 1} & 37 & {- 1} & {- 1} & {- 1} & 0 & {\quad 0} & {- 1} & {- 1} & {- 1} \\23 & {- 1} & 29 & {- 1} & 15 & {- 1} & 30 & {- 1} & 66 & {- 1} & 24 & {- 1} & 50 & {- 1} & 62 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} & {- 1} \\{- 1} & 30 & {- 1} & 65 & {- 1} & 54 & {- 1} & 14 & {- 1} & 0 & {- 1} & 30 & {- 1} & 74 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} \\32 & {- 1} & 0 & {- 1} & 15 & {- 1} & 56 & {- 1} & 85 & {- 1} & 5 & {- 1} & 6 & {- 1} & 52 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} \\{- 1} & 0 & {- 1} & 47 & {- 1} & 13 & {- 1} & 61 & {- 1} & 84 & {- 1} & 55 & {- 1} & 78 & {- 1} & 41 & X & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0}\end{bmatrix}\quad$

Further, ‘0’ denotes a 96×96 identity matrix, ‘−1’ denotes a 96×96 zeromatrix, an integer greater than or equal to 1 denotes a permutationmatrix formed by shifting each row of the 96×96 identity matrix in thesame direction, the same number of row intervals as the integer, ‘X’,which is between 0 and 95.

In another aspect of the present invention, an encoder is provided whichincludes a parity check matrix generation module for generating a paritycheck matrix by expanding a base matrix having each element possesspermutation information for identifying a permutation matrix formed bypermuting the base permutation matrix, and an encoding module forencoding input source data with the parity check matrix.

In another aspect of the present invention, a method of decoding datausing low density parity check (LDPC) code is provided, the methodcomprising providing a permutation matrix, a zero matrix and a basematrix generating a parity matrix by expanding the base matrix using thepermutation matrix, zero matrix; and using the parity matrix to decodedata

In another aspect of the present invention, a method of decoding inputsource data using low density parity check (LDPC) code is defined by abase matrix having each element possesses permutation information foridentifying a permutation matrix formed by shifting each row of the basepermutation matrix a certain number of row intervals in the samedirection. The method includes the following base matrix of which eachelement is a 96×96 permutation matrix: $\begin{bmatrix}2 & {- 1} & 19 & {- 1} & 47 & {- 1} & 48 & {- 1} & 36 & {- 1} & 82 & {- 1} & 47 & {- 1} & 15 & {- 1} & X & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 69 & {- 1} & 88 & {- 1} & 33 & {- 1} & 3 & {- 1} & 16 & {- 1} & 37 & {- 1} & 40 & {- 1} & 48 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\10 & {- 1} & 86 & {- 1} & 62 & {- 1} & 28 & {- 1} & 85 & {- 1} & 16 & {- 1} & 34 & {- 1} & 73 & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 28 & {- 1} & 32 & {- 1} & 81 & {- 1} & 27 & {- 1} & 88 & {- 1} & 5 & {- 1} & 56 & {- 1} & 37 & {- 1} & {- 1} & {- 1} & 0 & {\quad 0} & {- 1} & {- 1} & {- 1} \\23 & {- 1} & 29 & {- 1} & 15 & {- 1} & 30 & {- 1} & 66 & {- 1} & 24 & {- 1} & 50 & {- 1} & 62 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} & {- 1} \\{- 1} & 30 & {- 1} & 65 & {- 1} & 54 & {- 1} & 14 & {- 1} & 0 & {- 1} & 30 & {- 1} & 74 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} \\32 & {- 1} & 0 & {- 1} & 15 & {- 1} & 56 & {- 1} & 85 & {- 1} & 5 & {- 1} & 6 & {- 1} & 52 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} \\{- 1} & 0 & {- 1} & 47 & {- 1} & 13 & {- 1} & 61 & {- 1} & 84 & {- 1} & 55 & {- 1} & 78 & {- 1} & 41 & X & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0}\end{bmatrix}\quad$

In this method, ‘0’ denotes a 96×96 identity matrix, ‘−1’ denotes a96×96 zero matrix, an integer greater than or equal to 1 denotes apermutation matrix formed by shifting each row of the 96×96 identitymatrix in the same direction and the same number of row intervals as theinteger, ‘X’, which is between 0 and 95.

In another aspect of the present invention, a decoder is provided whichincludes a parity check matrix generation module for generating a paritycheck matrix by expanding a base matrix having each element possesspermutation information for identifying a permutation matrix formed bypermuting the base permutation matrix, and a decoding module forencoding input source data with the parity check matrix.

In another aspect of the present invention, an apparatus for encodingdata using low density parity check (LDPC) code is provided, theapparatus comprising a data source adapted to provide data to betransmitted, an LPDC encoder adapted to generate a parity matrix byexpanding the base matrix using a permutation matrix and a zero matrixand encode the data to be transmitted using the parity matrix, amodulation module adapted to modulate the encoded data to generatemodulated encoded data; and an antenna adapted to transmit the modulatedencoded data.

In another aspect of the present invention, an apparatus for decodingdata using low density parity check (LDPC) code is provided, theapparatus comprising an antenna adapted to receive modulated encodeddata, a demodulation module adapted to demodulate the modulated encodeddata to generate encoded data; and an LPDC decoder adapted to generate aparity matrix by expanding the base matrix using a permutation matrixand a zero matrix and decode the encoded data using the parity matrix.

It is to be understood that both the foregoing general description andthe following detailed description of the present invention areexemplary and explanatory and are intended to provide furtherexplanation of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this application, illustrate embodiment(s) of the invention andtogether with the description serve to explain the principle of theinvention. In the drawings;

FIG. 1 is a schematic diagram of a wireless communication system.

FIG. 2 illustrates a relationship of H=[H_(d)|H_(p)].

FIG. 3 illustrates a structure of a dual diagonal matrix.

FIG. 4 illustrates H^((i)) _(d) having 16 sub-matrices, i.e., (1, 1),(1, 2), . . . , (4, 4) when m=4.

FIG. 5 illustrates a parity check matrix H when r=½.

FIG. 6 is a flowchart illustrating generating a parity check matrix H.

FIG. 7 shows a parity check matrix H which includes a plurality of z×zpermutation matrices or zero matrices.

FIG. 8 shows a base matrix H_(b).

FIG. 9 illustrates another embodiment of encoding and decoding methodusing LDPC code.

FIG. 10 a illustrates an example for generating a second base matrix ofa 5×5 second base permutation matrix from a first base matrix of a 12×12first base permutation matrix.

FIG. 10 b illustrates a method for generating a second base matrix for a5×5 second base permutation matrix from a first base matrix of a 12×12first base permutation matrix according to Equation 5.

FIG. 11 is a structural diagram of a preferable embodiment of anencoding module using the LDPC code.

FIG. 12 is a structural diagram of a preferred embodiment of an encodingmodule.

FIG. 13 illustrates a line graph depicting a simulation of a groupingmethod using a modulo method and a flooring method.

FIGS. 14 a-14 f illustrates preferred embodiments of the base matrixH_(b) having functions.

FIG. 15 illustrates an embodiment of a base matrix H_(b) when the coderate is ½.

FIG. 16 illustrates another embodiment of the base matrix H_(b) when thecode rate is ⅔.

FIG. 17 illustrates another embodiment of the base matrix when the coderate is ¾.

FIG. 18 illustrates another embodiment of the base matrix when the coderate is ½.

FIG. 19 illustrates another embodiment of the base matrix when the coderate is ½.

FIG. 20 illustrates another embodiment of the base matrix when the coderate is ½.

FIG. 21 illustrates another embodiment of the base matrix when the coderate is ⅔.

FIG. 22 illustrates another embodiment of the base matrix when the coderate is ¾.

FIG. 23 illustrates another embodiment of the base matrix when the coderate is ¾.

FIG. 24 illustrates another embodiment of the base matrix when the coderate is ⅔.

FIG. 25 illustrates another embodiment of the base matrix when the coderate is ⅔.

FIG. 26 illustrates another embodiment of the base matrix when the coderate is ⅔.

FIG. 27 illustrates another embodiment of the base matrix.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Reference will now be made in detail to the preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

FIG. 1 is a schematic diagram of a wireless communication system inwhich embodiments of the present invention may be implemented. In FIG.1, a transmitter 10 and a receiver 30 communicate via a wireless channel20. From a data source 11 in the transmitter 10, a source data ‘u’ of kbits is processed by an LDPC encoder 13 such that the source data isencoded and processed as codeword ‘c’ of n bits. The codeword ‘c’ isthen transmitted by an antenna 17 after being modulated for wirelesstransmission by a modulation module 15. The signal transmitted via thewireless channel 20 is received by an antenna 31 in receiver 30.Thereafter, in receiver 30, an inverse operation is performed from thatof the transmitter 10. For example, a demodulation module 33 demodulatesthe received signal before from forwarding codeword c of n bits to anLDPC decoder 35. The process of data transmission/reception is notlimited to the above described example. The above described process is asimplified example to explain the embodiments of the present invention.

The embodiments of the present invention are directed to a specificoperation of encoding and decoding using the LDPC code in the LDPCencoder 13 and the LDPC decoder 35. In addition, the embodiments aredirected to a detailed description of an encoder and a decoder such asthe LDPC encoder 13 and the LDPC decoder 35. The following are detailedexamples of the embodiment.

Equation 3 shows calculation of code rate. In calculating the code rate,a transmitter takes into account factors, such as channel status andamount of transmission data.r=k/n  [Equation 3]

Here, ‘k’ represents the length of a source data, and n represents thelength of an encoded data (or codeword).

The encoded data (or codeword) includes systematic bits and parity checkbits. The systematic bits indicate pre-encoded source data, and theparity check bits indicate a series of bits which are decided bysystematic bits and Generate Matrix and are added to the back portion ofthe systematic bits. The value ‘n’ in the equation indicates the numberof bits added between the systematic bits and the parity check bits. Thenumber of parity check bits is reduced to increase the code rate of theLDPC code, and the number of systematic bits is reduced in order todecrease the code rate of the LDPC code.

With respect to an encoding method using LDPC code, the input sourcedata can be encoded using the generator matrix G based on Equation 1 andEquation 2. More specifically, the input source data S_(1×k) of the kbit is encoded through Equation 2 and becomes codeword X_(1×k) of the nbit. The codeword x includes x=[s p]=[s₀, s₁, . . . , S_(k−1), P₀, P₁, .. . , P_(m−1)]. Here, (p₀, p₁, . . . , p_(m−1)) represents parity checkbits and (s₀, s₁, . . . , s_(k−1)) represents systematic bits.

However, an encoding method using the generator matrix G is complex. Inorder to minimize such complexity, rather than relying on the generatormatrix G, it is preferable to use a parity check matrix H to directlyencode the input source data. Since x=[s p], using H·x=0, H·x=H·[s p]=0.From these relationships, the parity check bit p can be acquired and,consequently, codeword x=[s p] can be determined.

After the parity check matrix H is generated, the input source data isencoded using the generated parity check matrix H (S45).

Similar to the method used in the receiver 30 in FIG. 1, the followingequation is used to decode the encoded data:H·x=0  [Equation 4]

Equation 4 describes how to detect decoding error. More specifically, ifthe decoded data x and the parity check matrix H are multiplied and theoutcome is 0, the result signifies that there is no transmission error.However, if the outcome is a number other than 0, it signifies thatthere is transmission error.

FIGS. 11 and 12 are block diagrams of embodiments of an encoder 130 anda decoder 350, similar to, respectively, the LDPC encoder 13 and theLDPC decoder 35 of FIG. 1.

In Equation 1, the parity check matrix H can be expressed asH=[H_(d)|H_(p)], where H_(d) has a (n−k)×k dimension and H_(p) has a(n−k)×(n−k) dimension. FIG. 2 is an example illustrating therelationship of H=[H_(d)|H_(p)], where k represents the length of thesource data (in bits) which is encoded in the LDPC encoder 13 and nrepresents the length of the encoded codeword c (in bits).

From the relationship between Equation 1 and H=[H_(d)|H_(p)], theequation G=[I|(H_(p) ⁻¹H_(d))^(t)]^(t) can be determined. Furthermore,the LDPC encoder 13 performs the encoding operation by multiplyingG=[I|(H_(p) ⁻H_(d))^(t)]^(t) by the input source data u, in accordancewith Equation 2. Subsequently, Equation 2 can be expressed as thefollowing Equation 5:c=[I|(H _(p) ⁻¹ H _(d))^(t)]^(t) ·u  [Equation 5]

In this equation, if Hp has dual diagonal form, then Hp−1 is easilycalculated as lower triangular.

In addition to performing encoding operations by using the generatormatrix G, it is also possible to perform encoding operations by directlyencoding source data using the parity check matrix H.

Preferably, a (n−k)×(n−k) dual diagonal matrix can be used with H_(p).Regardless of the dimension of the matrix, the dual diagonal matrixrepresents a matrix in which all elements of a main diagonal and adiagonal immediately above or below the main diagonal are ‘1’s while theother elements are ‘0’s. FIG. 3 illustrates the structure of an exampleof the dual diagonal matrix.

A code rate is considered an important parameter in a method of encodingand decoding using the LDPC code. Specifically, each code rate r shouldbe supported by various codeword sizes, n. Usually, the values of ‘r’are r=½, ⅔, or ¾, but the values of ‘r’ are not limited to these values.As for ‘n,’ n=24*z (here, z=24+4*i, where i=0, 1, 2, 3, 4, . . . , 18)is often used. Different base matrices can be used for each ‘r’ and ‘n’to optimize encoding and decoding performances. However, if one basematrix H_(b) is used for all ‘n’ with respect to a specific ‘r,’ the useof memory may be decreased. Therefore, it is important to determine howto modify the permutation information included in one base matrix H_(b)to other n's.

The embodiment below provides for storing the first base matrix and thefirst base permutation matrix having a largest dimension (z_(max)) whileusing the first base matrix for encoding and decoding the base matrix ofa second base permutation matrix having other dimensions (z).

An example of a method of storing the first base matrix of the firstbase permutation matrix having a largest dimension (z_(max)) andgenerating using the first base matrix for encoding and decoding thebase matrix of a second base permutation matrix having other dimensions(z) will be described below.

FIG. 8 shows an example of a base matrix H_(b). The base matrix shown inFIG. 8 is merely an example, and the actual size of the base matrixH_(b) used in encoding and decoding is much larger. In FIG. 8, Z_(max)is 12. As such, the base matrix H_(b) has a base permutation matrixhaving a 12×12 dimension, a plurality of permutation matrices which isformed by circular shifting each row of the base permutation matrix aspecified interval in a certain direction, and a zero matrix. Forexample, ‘11’ in the base matrix H_(b) signifies the permutation matrixformed by circular shifting each row of the base permutation matrix 11intervals (of rows or columns) in a specified direction.

FIG. 9 illustrates another embodiment of encoding and decoding methodusing LDPC code. The following example of FIG. 9 is based on thecommunication system of FIG. 1. In order to perform encoding operation,the LDPC encoder should include the first base permutation matrix havingthe largest dimension (z_(max)) and the first base matrix of the firstbase permutation matrix. The first base permutation matrix shouldpreferably be an identity matrix. If a fixed matrix such as an identitymatrix is used as the first permutation matrix, the LDPC encoder doesnot need to store the information of the first base permutation matrix.

It is possible for the transmitter 10 to transmit through a channelafter the input source data has been encoded by using a generated Hmatrix by using the first base matrix. However, there are situationswhen an encoded input source data (codeword) is transmitted to thereceiver 30 after the H matrix is generated by using the second basematrix of the second permutation matrix. The dimension size of thesecond permutation matrix is ‘z’ which is smaller in size than thelargest dimension z_(max).

When defining the base matrix H_(b) according to (H_(b))_(d) and(H_(b))_(p), it is preferable to use a block dual diagonal matrix for(H_(b))_(p). More specifically, (H_(b))_(d) and (H_(b))_(p) is a part ofthe base matrix H_(b) represented by H=[(H_(b))_(d)|(H_(b))_(p)]. Theblock dual diagonal matrix has a main diagonal and diagonals immediatelyabove or below the main diagonal all forming an identity matrix whilethe rest being ‘0’. If (H_(b))_(p) is set to the block dual diagonalmatrix, H_(p) can have column weights of ‘1’ and in order to avoid this,one or two zero matrix should be replaced with the identity matrix,preferably.

(H_(b))_(d) of the base matrix H_(b) is formed by a combination of abase permutation matrix, a plurality of permutation matrices formed bycircular shifting each row of the base permutation matrix a specifiednumber of row intervals in a certain direction, and the zero matrix. Itis preferable to consider the operation of encoding and decoding whichprovides the best performance when forming the base matrix H_(b) bycombining the above described permutation matrices.

In the H matrix, H_(d) can be comprised of at least one H^((i)) _(d),where i=1, 2, . . . , r/(1−r), according to code rate (r=k/n). The coderate ‘r’ is determined by ‘k’ which is the length of source data and ‘n’which is the length of encoded codeword ‘c.’ Generally, code rates suchas r=½, ⅔, ¾, ⅘ can be used. H^((i)) _(d) is a matrix having (n−k)×(n−k)dimension, and is represented by H_(d)=[H^((i)) _(d)|H⁽²⁾ _(d)| . . .|H^((r/(1−r))) _(d)].

Preferably, when each H^((i)) _(d) is divided into m×m sub-matriceshaving (n−k)/m×(n−k)/m dimensions, each row weight and column weight ofthe sub-matrix of the H_(d) is ‘1’. More specifically, each row andcolumn of the sub-matrix has an element of ‘1’ while the other elements‘0’s. Furthermore, if any two rows of the Hd are compared, these rows donot have more than one column having ‘1’ overlapping each other. InH_(d), no two rows has overlapping columns of ‘1’, when two rows have acolumn overlapping in H_(p). More specifically, if any two rows in H_(d)are compared, for example, a row can have ‘1’ at column 7 while theother row may also have ‘1’ at column 7. However, these two rows do nothave any other columns sharing ‘1’s. If this condition is satisfied, thesame concept applies to columns. In other words, no two columns has morethan one overlapping rows of ‘1’s.

FIG. 4 illustrates an example H^((i)) _(d) having 16 sub-matrices, i.e.,(1, 1), (1, 2), . . . , (4, 4) when m=4. Having ‘1’ as the row weightand column weights of each sub-matrix means that there is only one rowor column having ‘1’ in each sub-matrix while the rest of rows andcolumns having ‘0’. It is preferable for m to use ‘4’-‘12’, which everprovides the best performance.

In another example, the row weight or column weight of a sub-matrix ofH_(d) can be either ‘0’ or ‘1’. In other words, among the sub-matricesof H^((i)) _(d), there are sub-matrices having ‘0’or ‘1∞ for row weightand column weight. As such, it is preferable for H^((i)) _(d) to havesame number of sub-matrices having row and column weights of ‘0’ in therow and column direction of H^((i)) _(d).

FIG. 5 illustrates an example of a parity check matrix H when r=½, withH_(d) on the left side and a dual diagonal matrix H_(p) on the rightside. In FIG. 5, H_(d) is comprised of a 25 sub-matrices. Here, a boxlabeled ‘1’ represents a sub-matrix having row and column weights of ‘1’while a box labeled ‘0’ represents a sub-matrix having row and columnweights of ‘0’. In FIG. 5, a sub-matrix having row and column weights of‘0’ exists once per each row and column in H_(d).

FIG. 6 is a flowchart illustrating a process of generating a paritycheck matrix H. The examples describing the processes of generating aparity check matrix H is not limited to the example described below.

In the first process, all rows and column weights should be ‘0’ or ‘1’with respect to sub-matrix (1, 1) of H⁽¹⁾ _(d) (S51). A sub-matrix, suchas the sub-matrix (1, 1) of H⁽¹⁾ _(d), from which other sub-matrices aregenerated is referred to as a base permutation matrix. Furthermore, itis preferable for the base permutation matrix to use identity matrix.

Next, the process involves performing permutation operation to the rowsand columns of the base permutation matrix to sequentially generate eachsub-matrix of H⁽¹⁾ _(d) (S51-S53). Preferably, no two rows of H_(d)should have more than one column with overlapping ‘1’ in generating eachsub-matrix of H^((i)) _(d). The sub-matrix formed by permutationoperation of rows and columns of the base permutation matrix is referredto as a permutation matrix.

Furthermore, the rest of the H^((i)) _(d) are generated (S54) accordingto the first (S51) and second (S52) processes (S53). Also, all of theH^((i)) _(d) are combined to generate H_(d) (S55). Finally, H_(d) andH_(p) are combined to generate H (S56).

FIG. 7 shows a parity check matrix H which includes a plurality of z×zpermutation matrices or a zero matrices. In FIG. 7, P_(i,j) represents az×z permutation matrix or a zero matrix.

When defining the base matrix H_(b) according to (H_(b))_(d) and(H_(b))_(p), it is preferable to use a block dual diagonal matrix for(H_(b))_(p). More specifically, (H_(b))_(d) and (H_(b))_(p) is a part ofthe base matrix H_(b) represented by H=[(H_(b))_(d)|(H_(b))_(p)]. Theblock dual diagonal matrix has a main diagonal and diagonals immediatelyabove or below the main diagonal all forming an identity matrix whilethe rest being ‘0’. If (H_(b))_(p) is set to the block dual diagonalmatrix, H_(p) can have column weights of ‘1’ and in order to avoid this,one or two zero matrix should be replaced with the identity matrix,preferably.

(H_(b))_(d) of the base matrix H_(b) is formed by a combination of abase permutation matrix, a plurality of permutation matrices formed bycircular shifting each row of the base permutation matrix a specifiednumber of row intervals in a certain direction, and the zero matrix. Itis preferable to consider the operation of encoding and decoding whichprovides the best performance when forming the base matrix H_(b) bycombining the above described permutation matrices.

With respect to the base matrix H_(b), a difference in number of any twopermutation information from the permutation information has to be belowa selected first critical value. In other words, the number of eachpermutation matrix should be same or similar with respect to the basematrix H_(b). Preferably, the value of the first critical value shouldbe small but the value can be between 3-7

With respect to the parity check matrix H, it is preferable to preventor minimize the occurrence of a 4-cycle or a 6-cycle. In particular, itis preferable for the parity check matrix H not to have the 4-cycle.Furthermore, it is preferable for the parity check matrix H to have6-cycles less than a selected second critical value. When any two rowsof the parity check matrix H has ‘1’ at the same two columns, this iscalled the 4-cycle. Similarly, the 6-cycle is when any three rows of theparity check matrix have ‘1’ at the same two columns based on anycombinations of two rows.

In addition, with respect to Hd in the parity check matrix H, the rowweight and the column weight should have regularity which refers to sameweight in all rows and in all columns respectively, because of lowcomplex implementation without performance degradation. If a z×zidentity matrix is used as the base permutation matrix, the parity checkmatrix H can have regularity in the row weight and the column weight.

The base matrix H_(b) should be formed to achieve effective encoding anddecoding performance for all code rates and codeword sizes. Becausevariable code rates and codeword sizes are being applied to mobilecommunication systems, the base matrix should be formed to achieveoptimum performance for all code rate and codeword sizes when the basematrix H_(b) is formed based on the combination of the base permutationmatrix, the plurality of permutation matrices, and the zero matrices.

Each element of the first base matrix can have two or more permutationinformation. More specifically, the entire range of dimensions of thechanging base permutation matrix can be divided into two or more smallerranges in order that each range carries the optimum permutationinformation. For example, if the range of the changing dimension z is10-96, the range is divided into two smaller ranges of dimensions. Thefirst range includes 10-53 and the second range includes 54-96.Subsequently, the optimized first base matrix is assigned to eachdimension. Although there are now two first base matrices, each firstbase matrix needs not to be independently stored and the elements of thefirst base matrix can store information of two first base matrices. As aresult, performance of encoding and decoding is enhanced while requiringless memory.

An element of the parity check matrix H can be expressed by a basematrix H_(b) which includes the permutation information used to identifya plurality of permutation matrices formed by permutation of row andcolumns of the base permutation matrix.

With respect to encoding and decoding using parity check matrix H in theLDPC encoder 13 or the LDPC decoder 35 in FIG. 1, the parity checkmatrix H can be generated after expanding the base matrix H_(b) by usingthe base permutation matrix and the permutation information. Moreover,it is preferable to use the generated parity check matrix to performencoding and decoding operation.

By expanding the base matrix H_(b), it means that z×z matrix, whichsignifies the permutation information, replaces each element of the basematrix H_(b). The z×z matrix refers to permutation matrix, or zeromatrix. Here, based on the expansion of the base matrix H_(b), theparity check matrix H is subsequently generated.

It is also possible to consider a different process for generating the Hmatrix from the base matrix H_(b). First, ‘−1’ is designated to ‘zeromatrix’ and all other permutation information other than those of “−1”are designated to a binary base matrix H_(bin), which has the samematrix dimension as H_(b) having “1” designation. Furthermore, ifH_(bin), is used to generate the H matrix, the process of H_(bin)generating H_(b) is added. The process of generating the H matrix issame as above after H_(b) is acquired.

As explained above, a plurality of permutation matrices are permuted andformed based on a specific method from at least one base permutationmatrix. Preferably, a base permutation matrix is an identity matrix.Moreover, it is preferable for at least one base permutation matrix andthe plurality of permutation matrices to have row and column weight of‘1’. In other words, it is preferable to have only one element having‘1’ while the other elements are ‘0’ from the elements of all rows andcolumns of the plurality of permutation matrices.

A method of circular shifting each entire row or column of the basepermutation matrix a specified interval in a specific direction can beconsidered as the method for forming the plurality of permutationmatrices from the base permutation matrix.

The parity check matrix H can be defined by a base matrix H_(b) havingpermutation information as an element for identifying a base permutationmatrix or a permutation matrix formed by permutation of each row orcolumn of the base permutation matrix. The example provided belowillustrates a case where each row or column of the base permutationmatrix is shifted circularly a specified interval in a specifieddirection, for example, right or left, to form a plurality ofpermutation matrix from the base permutation matrix.

The first base matrix H_(b) for the base permutation matrix having thelargest dimension (z_(max)) is stored, and other base matrices for otherbase permutation matrices having smaller dimensions (z) are generatedfrom the first base matrix by replacing each permutation information ofthe first base matrix with a remainder of each permutation informationof the first base matrix divided by the value of ‘z.’

Depending on the size of codewords, it may be necessary to makedimensions of the base permutation matrix 5×5 during encoding anddecoding operation. In such a case, a modulo function ‘mod(A, B)’ can beused. Here, mod(A, B) indicates a remainder of A divided by B. In otherwords, with respect to the 5×5 base permutation matrix, ‘11’ in the basematrix H_(b) does not mean that each row of the base permutation matrixhaving a dimension size of 5×5 is shifted 11 intervals. Instead, itmeans that the rows are shifted ‘mod(11, 5)=1’ in the same direction.

The following example illustrates how to more efficiently generate theparity check matrix H and performing LDPC encoding and decodingoperation based on the generated parity check matrix H when thedimensions (or value of ‘z’) of the base permutation matrix changes dueto varying lengths of the codeword. The examples provided relate togenerating a second base matrix based on different dimensions (z) of thebase permutation matrix by using a first base matrix. Moreover, thesecond base matrix is generated by a similar shift pattern to that ofthe first base matrix, and consequently is able to enhance encoding anddecoding performance.

In FIG. 9, the first base matrix is used by the transmitter 10 togenerate the second base matrix (S41). The generation method of thesecond base matrix is explained by using the base matrix illustrated inFIG. 8. In FIG. 8, the size of the largest dimension z_(max) is 12.Accordingly, the first base matrix H_(b) is formed by indexinginformation. The indexing information comprises a 12×12 first basepermutation matrix, a plurality of permutations formed by shiftingcircularly each row of the base permutation matrix a certain number ofrow intervals in a specified direction, and a zero matrix. For example,‘11’ in the base matrix H_(b) signifies the permutation matrix formed byshifting circularly the base permutation matrix 11 intervals (of rows orcolumns) in a specified direction.

FIG. 10 a illustrates a method for generating a second base matrix of a5×5 second base permutation matrix from a first base matrix of a 12×12first base permutation matrix. If the dimension size (z) of the secondbase permutation is made smaller according to the size of codewordduring the encoding operation in the transmitter, as depicted in FIG. 10a, a grouping method is used. In other words, ‘0,’ ‘1,’ and ‘2’ of thefirst base matrix are grouped and mapped as ‘0’ in the second basematrix. Similarly, ‘3’ and ‘4’ of the first base matrix are grouped andmapped as ‘1’ while ‘5’ and ‘6’ are grouped and mapped as ‘2.’ The samepattern of grouping and mapping is repeated such that ‘7,’ ‘8,’ and ‘9’are grouped and mapped as ‘3’ and ‘10’ and ‘11’ are grouped and mappedas ‘4.’ As a result of grouping and mapping, the second base matrix isgenerated.

In the grouping method, the permutation matrix of the first basepermutation matrix having neighboring shift numbers is mapped to onepermutation matrix of the second base permutation matrix. Furthermore,the grouping method is designed to maintain most of the base features ofthe first base matrix in generating the second base matrix. In FIG. 10a, at least two permutation matrix of the first base permutation matrixis grouped and mapped to one permutation matrix in the second basepermutation matrix. However, it is possible to map one permutationmatrix of the first base permutation matrix to one permutation matrix ofthe second base permutation matrix.

For a specific grouping method, a flooring function can be used asdefined in Equation 6:Shift(z)=floor(shift(z _(max))z/z _(max))  [Equation 6]

In this equation, shift(z) denotes a number of shifted row intervals inthe z×z permutation matrix. Also in the equation, floor(x) denotes anearest integer from x approaching negative infinity.

FIG. 10 b illustrates a method for generating a second base matrix for a5×5 second base permutation matrix from a first base matrix of a 12×12first base permutation matrix according to Equation 5.

For example, a permutation matrix which has been generated by mapping apermutation matrix formed by shifting each row of the 12×12 first basepermutation matrix 7 intervals to a 5×5 second base permutation matrix.This permutation can be expressed using Equation 6 as:Shift(5)=floor(shift(12)×5÷12)=floor(7×5÷12)=Floor(2.92)=2

In other words, the permutation matrix, formed by shifting circularlyeach row of the 12×12 first base matrix 7 intervals, is mapped to apermutation matrix having each row of the 5×5 second permutation matrixshifted 2 intervals.

By using a generating method as explained above, the second base matrixcan be generated by replacing each element of the first base matrix withelements of the second base matrix. It is possible to simplify thecomplexities by implementing the flooring function to hardware orsoftware.

After the second base matrix is generated (S41), a parity check matrix Hcan be generated using the second base permutation matrix and the secondbase matrix (S43). The second base matrix can generate the parity checkmatrix H having a z×z dimension size by using the second basepermutation matrix and the second base matrix. The second base matrixincludes a zero matrix, identity matrix, or permutation matrix formed byshifting circularly all the rows of the second base permutation matrix aspecified interval.

It is possible to perform the second base matrix generation procedure(S41) and the parity check matrix H generation procedure (S43)concurrently. It is also possible to generate the parity check matrix Hby replacing each element of the second base matrix, which was acquiredthrough Equation 6, with the corresponding elements of the zero matrix,base permutation matrix, or permutation matrix.

As described above, it is preferable for the base permutation matrix toperform a generation operation, first by considering the use of memoryin the memory module and storing only the first base matrix of the firstbase permutation matrix having the largest dimension (z_(max)) andsecond by using the first base matrix for encoding and decoding in thebase matrix of the second base permutation matrix having other dimensionsizes (z). It is also preferable to set different dimension sizes of thebase permutation matrix according to changes in the lengths ofcodewords.

FIG. 13 illustrates a line graph depicting a simulation of a groupingmethod using a modulo function and a flooring function. Here, the graphindicates the superior performance of the flooring method compared tothe modulo function.

FIG. 11 is a structural diagram of a preferable embodiment of anencoding module using the LDPC code. The encoder 130 includes a memorymodule 131, a base matrix generation module 132, a parity check matrixgeneration module 133, and an encoding module 134. The memory module 131stores information related to the first base permutation matrix, thesecond base permutation matrix, and the first base matrix. The basematrix generation module 132 generates a second base matrix using theinformation of the first base permutation matrix and the first basematrix whose information is stored in the memory module 131. The paritycheck matrix generation module 133 generates a parity check matrix usingthe information of the second base permutation matrix, the second basematrix generated from the base matrix generation module 132 whoseinformation is stored in the memory module 131. The encoding module 134encodes the input source data using the parity check matrix generatedfrom the parity check matrix module 133.

If the length of the codeword does not change, the memory module storesone base permutation matrix information and one base matrix informationand the base matrix generation module is not necessary. Furthermore, ifa simple matrix such as an identity matrix is used in the first orsecond permutation matrix, the memory module 131 does not have to storeinformation of the first or second base permutation matrix. Thefunctions of the base matrix generation module 132, the parity matrixgeneration module 133, and the encoding module 134 can be implemented insoftware or hardware based on the functions of each module.

FIG. 12 is a structural diagram of a preferred embodiment of a decodingmodule. The encoder 350 includes a memory module (351), a base matrixgeneration module (352), a parity check matrix generation module (353),and an encoding module (354). The function of the memory module 351, thebase matrix generation module 352, and the parity check matrixgeneration module 353 are the same as the corresponding modules of FIG.11. The encoding module 354 encodes the input data by using the paritycheck matrix generated by the parity check matrix generation module 353.The explanation provided with respect to the functions in FIG. 11applies to FIG. 12.

The following is a detailed description of the base permutation matrixand the base matrix in order to effectuate better performance inencoding and decoding methods using the LDPC code.

FIGS. 14 a-14 f illustrates preferred embodiments of the base matrixH_(b) having functions as described above. In FIGS. 14 a-14 f, a coderate is ¾. When the code rate is ¾, with respect to the base matrix, ‘0’signifies an identity matrix having a z×z dimension, ‘−1’ signifies azero matrix having a z×z dimension, and an integer greater than 1signifies a permutation matrix formed by each row (or column) of the z×zidentity matrix shifted circularly in a specified direction (i.e., rightor left). The number of rows or columns shifted corresponds to the valueof the integer. For example, if the integer is 5, then the rows (orcolumns) are shifted 5 intervals.

As illustrated in FIG. 15, if the code rate is ½, the size of the basematrix can be shortened from that of the base matrix for the ¾ code rateto form the base matrix H_(b).

FIG. 16 is another embodiment of the base matrix H_(b). The illustrationof the base matrix is based on a code rate of ⅔. As described above withrespect to FIGS. 14 a-14 f, the significance and effects of ‘0,’ ‘−1,’and integer greater than or equal to 1 are the same.

FIG. 17 illustrates another embodiment of a base matrix for code rate ¾.In this embodiment, a number of 4-cycle and 6-cycle is minimized in thebase matrix and the column weight is given regularity. Furthermore, inorder for all code rates and codeword sizes to attain optimumperformance, each element of the base matrix shifts the base permutationmatrix. Comparing FIG. 17 to FIGS. 14 a-14 f, the performance of thematrix is comparable to that of the FIGS. 14 a-14 f despite having ¼ thesize.

FIG. 18 illustrates another embodiment of a base matrix for code rate ½.In FIG. 18, the base matrix is designed to perform parallel processingmore effectively. More specifically, when a sequential row order of(1→7→2→8→3→9→4→10→5→11→6→12) is set in the base matrix, the ‘non-zero’elements of any two rows do not overlap and, at the same time, theelements do not overlap in any columns of the two rows. A ‘non-zero’element refers to all other elements other than the elements of the zeromatrix in the base matrix. For example, in FIG. 18, if row 8 is comparedto either row 2 or row 3, the ‘non-zero’ element does not overlap in anycolumns of the compared rows.

FIG. 19 illustrates another embodiment of a base matrix for code rate ½.For a more effective parallel processing, the base matrix is designed sothat ‘non-zero’ elements of two sets of rows, such as (1, 7), (2, 8),(3, 9), (4, 10), (5, 11), (6, 12), do not overlap with any columns ofthese rows. As shown by the embodiments of FIGS. 18 and 19, it ispossible to implement an effective parallel processing during decoding.

FIGS. 20-22 illustrate other embodiments of a base matrix for code rates½, ⅔, and ¾, respectively. In these figures, the base matrices provideeffective performance after the base matrix is expanded to a z×z basepermutation.

FIG. 23 illustrates another embodiment of a base matrix for code rate ¾.The base matrix is expanded by the base permutation matrix of alldimensions (z). Particularly, when z=56, performance is optimized.

FIGS. 24 and 25 illustrate other embodiments of a base matrix for coderate ⅔. The embodiments are designed to have irregular column weightsfor enhanced performance. In particular, FIG. 25 illustrates shortcodeword lengths such as c=576 or c=672.

FIG. 26 illustrates another embodiment of a base matrix for code rate ⅔.‘X’ denotes an integer from 0 to 95 and, preferably, X may be 86, 89, or95. The most preferable value is X=95. The base matrix in FIG. 26 has aparallel processing feature and is designed for effective performance.The parallel processing feature can significantly decoding operationtime and more specifically, when each row is indexed in the order of 1,2, 3, 4, 5, 6, 7, and 8, the ‘non-zero’ elements are non-overlappingbetween the rows of the generated matrix, which is generated fromexchanging rows with neighboring rows. The ‘non-zero’ element refers toa shift number from 0-95, excluding −1. Furthermore, the neighboringcells indicate a non-overlapping ‘non-zero’ element between the firstand last rows in the matrix generated by exchanging rows. An example ofthe base matrix in FIG. 26 that satisfies the above conditions is1−4−7−2−5−8−3−6−(1) as illustrated in FIG. 27.

In FIG. 27, all the base matrix generated by exchanging rows in the basematrix have the same LDPC code as the LDPC code defined by the basematrix of FIG. 26. Moreover, with respect to encoding and decoding, evenusing the base matrix after the rows have been exchanged, theperformance of the encoding and decoding operation can be the same asthat of the base matrix of FIG. 26.

In the context of performance, a good performance is synonymous with alow Frame Error Rate (FER).

In the following description, a method of transmitting and receivingdata which is encoded by LDPC code is introduced. More specifically, thebase permutation matrix and the permutation information included in thebase matrix is used to expand the base matrix. After the parity checkmatrix H is generated, the parity check matrix H is used to encode ordecode the input source data. The examples provided hereinafter withrespect to the method of encoding and decoding can be referenced to theIEEE 802.16e specification and relate to encoding and decoding used intransmitting data between a mobile subscriber station (MSS) and a basestation (BS) in a Broadband Wireless Access System.

When the MSS enters a cell, the MSS transmits and receives the SBC-REQand SBC-RSP messages with the BS in order to negotiate the capabilitiesof the MSS and the BS. Table 1 and Table 2 show the format of theSBC-REQ and SBC-RSP messages, respectively. TABLE 1 Syntax Size NotesSBC-REQ_Message_Fromat( ){  Management Message Type = 26 8 bits  TLVEncoded Information variable TLV specific }

TABLE 2 Syntax Size Notes SBC-RSP_Message_Fromat( ){  Management MessageType = 27 8 bits  TLV Encoded Information variable TLV specific }

The functions of the MSS and the BS include the TLV message. A channelcoding scheme supported by the MSS and the BS is included in the TLVfield.

Table 3 and Table 4 show the formats of the TLV fields. Specifically,Tables 3 and 4 indicate demodulator options for downlink data receptionand modulator options for uplink data transmission which can be found inthe IEEE 802.16e specification. In Tables 3 and 4, a bit value of ‘0’indicates that the corresponding demodulating scheme is not supportedand a bit value of ‘1’ indicates that the corresponding modulatingscheme is supported. TABLE 3 Type Length Value Scope 151 1 bit Bit #0:64-QAM SBC-REQ Bit #1: BTC SBC-RSP Bit #2: CTC Bit #3: STC Bit #4: AASDiversity Map Scan Bit #5: AAS Direct Signaling Bit #6: H-ARQ Bit #7:Reserved; shall be set to zero Bits# 8: LDPC Bits#9-15: Reserved; shallbe set to zero

TABLE 4 Type Length Value Scope 152 1 Bit# 0: 64-QAM SBC-REQ Bit# 1: BTCSBC-RSP Bit# 2: CTC Bit# 3: AAS Diversity Map Scan Bit# 4: AAS DirectSignaling Bit# 5: H-ARQ Bits# 6: LDPC Bits# 7: Reserved; shall be set tozero 153 1 The number of HARQ ACK Channel SBC-REQ SBC-RSP

Although lower code rate generally means higher coding gain, the amountof data that can be transmitted in a given broadband decreases.Furthermore, the transmission rate is determined on the basis of thewireless channel status.

In a good wireless channel environment, more data can be transmitted ina given broadband by transmitting using a higher code rate. On thecontrary, in a poor wireless channel environment poor, the transmissionsuccess rate increases by transmitting using a lower code rate. Channelinformation is transmitted from the data receiving end to the datatransmitting end via a Channel Quality Indication Channel (CQICH). Thetransmitting end determines the modulation order by using methods suchas Quadrature Phase Shift Keying (QPSK), 16 Quadrature AmplitudeModulation (QAM), and 64 QAM, and determines the code rate based on theCQICH information and the available wireless resources.

If the MSS transmits data to the BS after channel coding by an encodingprocedure using the LDPC code, the MSS indicates that the data is LDPCchannel encoded through the Uplink Channel Descriptor (UCD) burstprofile encoding which is located before the data. The UCD includes coderate information. The BS uses the information received from the UCD todecode the data. Table 5 shows an example of an UCD burst profileencoding format. TABLE 5 Type Name (1 byte) Length Value FEC Code type150 1  0 = QPSK (CC) ½  1 = QPSK (CC) ¾  2 = 16-QAM (CC) ½  3 = 16-QAM(CC) ¾  4 = 64-QAM (CC) ⅔  5 = 64-QAM (CC) ¾  6 = QPSK (BTC) ½  7 = QPSK(BTC) ⅔  8 = 16-QAM (BTC) ⅗  9 = 16-QAM (BTC) ⅘ 10 = 64-QAM (BTC) ⅝ 11 =64-QAM (BTC) ⅘ 12 = QPSK (CTC) ½ 13 = QPSK (CTC) ⅔ 14 = QPSK (CTC) ¾ 15= 16-QAM (CTC) ½ 16 = 16-QAM (CTC) ¾ 17 = 64-QAM (CTC) ⅔ 18 = 64-QAM(CTC) ¾ 19 = 64-QAM (CTC) ⅚ 20 = QPSK (ZT CC) ½ 21 = QPSK (ZT CC) ¾ 22 =16-QAM (ZT CC) ½ 23 = 16-QAM (ZT CC) ¾ 24 = 64-QAM (ZT CC) ⅔ 25 = 64-QAM(ZT CC) ¾ 26 = QPSK (LDPC) ½ 27 = QPSK (LDPC) ⅔ 28 = QPSK (LDPC) ¾ 29 =16-QAM (LDPC) ½ 30 = 16-QAM (LDPC) ⅔ 31 = 16-QAM (LDPC) ¾ 32 = 64-QAM(LDPC) ½ 33 = 64-QAM (LDPC) ⅔ 34 = 64-QAM (LDPC) ¾ 35 = QPSK (LDPC) ⅔ 36= QPSK (LDPC) ¾ 37 = 16-QAM (LDPC) ⅔ 38 = 16-QAM (LDPC) ¾ 39 = 64-QAM(LDPC) ⅔ 40 = 64-QAM (LDPC) ¾ 41 . . . 255 = Reserved Ranging 151 1Reducing factor in units of 1 dB, between the data Ratio power used forthis burst and power should be used for CDMA Ranging. Normalized 152 5This is a list of numbers, where each number is C/N encoded by onenibble, and interpreted as a Override signed integer. The nibblescorrespond in order to the list define by Table 332, starting from thesecond line, such that the LS nibble of the first byte corresponds tothe second line in the table. The number encoded by each nibblerepresents the difference in normalized C/N relative to the previousline in the table.

If the BS transmits the LDPC channel coded data to the MSS, the BSindicates to the MSS that the data is LDPC channel encoded through aDownlink Channel Descriptor (DCD) burst profile encoding which islocated before the data. The DCD includes code rate and code rateinformation. The BS uses the information received from the DCD to decodethe data. Table 6 shows an example of a DCD burst profile encodingformat. TABLE 6 Name Type Length Value FEC Code 150 1  0 = BPSK (CC) ½Type  1 = QPSK (RS + CC/CC) ½  2 = QPSK (RS + CC/CC) ¾  3 = 16-QAM (RS +CC/CC) ½  4 = 16-QAM (RS + CC/CC) ¾  5 = 64-QAM (RS + CC/CC) ⅔  6 =64-QAM (RS + CC/CC) ¾  7 = QPSK (BTC) ½  8 = QPSK (BTC) ¾ or ⅔  9 =16-QAM (BTC) ⅗ 10 = 16-QAM (BTC) ⅘ 11 = 64-QAM (BTC) ⅔ 12 = 64-QAM (BTC)5/6 13 = QPSK (CTC) ½ 14 = QPSK (CTC) ⅔ 15 = QPSK (CTC) ¾ 16 = 16-QAM(CTC) ½ 17 = 16-QAM (CTC) ¾ 18 = 64-QAM (CTC) ⅔ 19 = 64-QAM (CTC) ¾ 20 =QPSK (ZT CC) ½ 21 = QPSK (ZT CC) ¾ 22 = 16-QAM (ZT CC) ½ 23 = 16-QAM (ZTCC) ¾ 24 = 64-QAM (ZT CC) ⅔ 25 = 64-QAM (ZT CC) ¾ 26 = QPSK (LDPC) ½ 27= QPSK (LDPC) ⅔ 28 = QPSK (LDPC) ¾ 29 = 16-QAM (LDPC) ½ 30 = 16-QAM(LDPC) ⅔ 31 = 16-QAM (LDPC) ¾ 32 = 64-QAM (LDPC) ½ 33 = 64-QAM (LDPC) ⅔34 = 64-QAM (LDPC) ¾ 35 = QPSK (LDPC) ⅔ 36 = QPSK (LDPC) ¾ 37 = 16-QAM(LDPC) ⅔ 38 = 16-QAM (LDPC) ¾ 39 = 64-QAM (LDPC) ⅔ 40 = 64-QAM (LDPC) ¾41 . . . 255 = Reserved DIUC 151 1 0-63.75 dB mandatory CINR at or belowwhere this DIUC can no exit longer be used and where this change to athreshold more robust DIUC is required, in 0.25 dB units. See FIG. 81.DIUC 152 1 0-63.75 dB minimum The minimum CINR required to start entryusing this DIUC when changing from threshold a more robust DIUC isrequired, in 0.25 dB units. See FIG. 81. TCS_enable 153 1 0 = TCSdisabled 1 = TCS enabled 2-255 = Reserved

The following is an explanation of a method of encoding a data using theLDPC code in the encoder of a transmitter. According to the IEEE 802.16especification, data is received in the physical layer from an upperlayer. Before encoding in the physical layer, the data goes throughseveral processes including padding, data randomization, and packetconcatenation processes. The padding process involves adding ‘I’ to therear portion of the data to satisfy the fixed size if the size of thedata received from the upper layer does not meet the size of the fixedchannel coding block. The data randomization process includes spreadingthe data in order to prevent a possible problem in clock recovery in thereceiving end when unmodulated symbols occur during transmission if theinput data has a fixed pattern. The packet concatenation processincludes setting the size of the encoding block to fit the givenbroadband size. The encoding block determined through these processes isone of {36, 42, 48, 54, 56, 60, 63, 64, 66, 72, 78, 80, 81, 84, 88, 90,96, 99, 102, 104, 108, 112, 114, 117, 120, 128, 132, 135, 136, 138, 144,152, 153, 160, 162, 168, 171, 176, 180, 184, 189, 192, 198, 207, 216}.The input source data of the encoder in the transmitting end isdetermined after the above-mentioned processes.

The encoded data is transmitted to the receiving end through thephysical channel. With respect to the IEEE 802.16e specification, theencoded data is mapped according to an Orthogonal Frequency DivisionMultiplexing symbol before transmission. Specifically, the modulationorder of the mapped symbol is determined after considering the size ofthe given broadband and the status of the transmission channel.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the inventions. Thus, itis intended that the present invention covers the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

1. A method of encoding data using low density parity check (LDPC) code,the method comprising: providing a permutation matrix, a zero matrix anda base matrix; generating a parity matrix by expanding the base matrixusing the permutation matrix and zero matrix; and using the paritymatrix to encode data to be transmitted.
 2. The method of claim 1,wherein the base matrix is expanded by replacing a value correspondingto each of first specified locations in the base matrix with one of thepermutation matrix and an altered permutation matrix based on thepermutation matrix, and replacing a value corresponding to each ofsecond specified locations in the base matrix with the zero matrix. 3.The method of claim 2, wherein each of the first specified locations isa location comprising a non-negative integer and each of the secondspecified locations is a location comprising a negative integer.
 4. Themethod of claim 2, wherein each location of the base matrix contains oneof a non-negative integer and “−1” and expanding the base matrixcomprises: replacing each location of the base matrix containing “−1”with the contents of the zero matrix; replacing each location of thebase matrix containing a positive integer with the permutation matrixaltered according to the positive integer; and replacing each locationof the base matrix containing a zero with the permutation matrix in anunaltered state.
 5. The method of claim 4, wherein the permutationmatrix is altered by circular shifting one of each entire row and eachentire column a number of intervals equal to the positive integer. 6.The method of claim 1, wherein the number of columns and the number ofrows of the permutation matrix are the same and are equal to the numberof columns and the number of rows of the zero matrix.
 7. The method ofclaim 1, wherein the permutation matrix is defined as having a rowweight and column weight of “1”.
 8. The method of claim 1, wherein thenumber of rows and the number of columns in the permutation matrix isequal to z and the number of rows of the base matrix is equal to thenumber of columns in the parity matrix divided by z and multiplied by(1−(a coding rate)).
 9. The method of claim 1, further comprising:providing a first base matrix, the first base matrix associated with afirst codeword length for a specified code rate and each locationcomprising a value; and generating a second base matrix by altering thevalue corresponding to each of specific locations of the first basematrix, the second base matrix associated with a second codeword length,wherein altering comprises flooring the value corresponding to each ofthe specific locations according to a number of columns and rows in afirst permutation matrix and a number of columns and rows in a secondpermutation matrix.
 10. The method of claim 9, wherein the parity matrixis generated by expanding the second base matrix using the secondpermutation matrix and the zero matrix.
 11. The method of claim 9,wherein altering is performed using a function comprising the form:shift(z)=floor (shift (z _(max))z/z _(max)) wherein z_(max) is thenumber of columns and rows in the first permutation matrix, z is thenumber of columns and rows in the second permutation matrix, shift(z_(max)) is the value corresponding to a specific location in the firstbase matrix, shift(z) is an altered value corresponding to the specificlocation in the second base matrix, and floor (x) is a flooring functionthat denotes the nearest integer from x toward negative infinity. 12.The method of claim 11, wherein z_(max) is
 96. 13. The method of claim9, wherein each of the specific locations is a location comprising apositive integer.
 14. The method of claim 9, wherein the first codewordlength is a maximum codeword length.
 15. The method of claim 9, whereinthe specified code rate is one of ½, ⅔ and ¾.
 16. The method of claim 9,wherein each location of the base matrix comprises one of a non-negativeinteger and “−1”.
 17. The method of claim 9, wherein the code rate is ⅔and the first base matrix comprises: $\begin{bmatrix}2 & {- 1} & 19 & {- 1} & 47 & {- 1} & 48 & {- 1} & 36 & {- 1} & 82 & {- 1} & 47 & {- 1} & 15 & {- 1} & 95 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 69 & {- 1} & 88 & {- 1} & 33 & {- 1} & 3 & {- 1} & 16 & {- 1} & 37 & {- 1} & 40 & {- 1} & 48 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\10 & {- 1} & 86 & {- 1} & 62 & {- 1} & 28 & {- 1} & 85 & {- 1} & 16 & {- 1} & 34 & {- 1} & 73 & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 28 & {- 1} & 32 & {- 1} & 81 & {- 1} & 27 & {- 1} & 88 & {- 1} & 5 & {- 1} & 56 & {- 1} & 37 & {- 1} & {- 1} & {- 1} & 0 & {\quad 0} & {- 1} & {- 1} & {- 1} \\23 & {- 1} & 29 & {- 1} & 15 & {- 1} & 30 & {- 1} & 66 & {- 1} & 24 & {- 1} & 50 & {- 1} & 62 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} & {- 1} \\{- 1} & 30 & {- 1} & 65 & {- 1} & 54 & {- 1} & 14 & {- 1} & 0 & {- 1} & 30 & {- 1} & 74 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} \\32 & {- 1} & 0 & {- 1} & 15 & {- 1} & 56 & {- 1} & 85 & {- 1} & 5 & {- 1} & 6 & {- 1} & 52 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} \\{- 1} & 0 & {- 1} & 47 & {- 1} & 13 & {- 1} & 61 & {- 1} & 84 & {- 1} & 55 & {- 1} & 78 & {- 1} & 41 & 95 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0}\end{bmatrix}\quad$
 18. A method of encoding or decoding data using lowdensity parity check (LDPC) code, the method comprising using a paritymatrix comprising a plurality of z-by-z zero sub matrices and aplurality of z-by-z permutation sub matrices.
 19. The method of claim18, wherein an m_(b)-by-n_(b) base matrix is expanded to generate anm_(b)*z-by-n_(b)*z parity matrix by replacing a value corresponding toeach of first specified locations in the base matrix with a permutationmatrix and replacing a value corresponding to each of second specifiedlocations in the base matrix with the zero matrix.
 20. The method ofclaim 19, wherein each of the first specified locations is a locationcomprising a non-negative integer and each of the second specifiedlocations is a location comprising a negative integer.
 21. The method ofclaim 19, wherein each location of the base matrix comprises one of anon-negative integer and “−1” and expanding the base matrix comprises:replacing each location of the base matrix containing “−1” with thecontents of a z-by-z zero sub matrix; replacing each location of thebase matrix containing a positive integer with a z-by-z permutation submatrix that is altered according to the positive integer; and replacingeach location of the base matrix containing a zero with an unalteredz-by-z permutation sub matrix
 22. The method of claim 21, wherein thez-by-z permutation sub matrix is altered by circular shifting one ofeach entire row and each entire column a number of intervals equal tothe positive integer.
 23. The method of claim 18, wherein the z-by-zpermutation sub matrix is defined as having a row weight and columnweight of “1”.
 24. The method of claim 18, further comprising: providinga first m_(b)-by-n_(b) base matrix, the first base matrix associatedwith a first codeword length for a specified code rate and each locationcomprising a value; generating a second an m_(b)-by-n_(b) base matrix byaltering the value corresponding to each of specific locations of thefirst base matrix, the second base matrix associated with a secondcodeword length, wherein altering comprises flooring the valuecorresponding to each of the specific locations according to a number ofcolumns and rows in a first permutation matrix and a number of columnsand rows in a second permutation matrix.
 25. The method of claim 24,wherein the parity matrix is generated by expanding the secondm_(b)-by-n_(b) base matrix using the second permutation matrix and thezero matrix.
 26. The method of claim 24, wherein altering is performedusing a function comprising the form:shift(z)=floor (shift(z_(max))z/z _(max)) wherein z_(max) is a number ofcolumns and rows in a first permutation matrix, z is a number of columnsand rows in a second permutation matrix, shift (z_(max)) is the valuecorresponding to a specific location in the first base matrix, shift(z)is an altered value corresponding to the specific location in the secondbase matrix, and floor (x) is a flooring function that denotes thenearest integer from x toward negative infinity; and utilizing thesecond base matrix to generate an m_(b)*z-by-n_(b)* parity matrix. 27.The method of claim 24, wherein each of the specific locations is alocation comprising a positive integer.
 28. The method of claim 26,wherein z_(max) is
 96. 29. The method of claim 24, wherein each locationof the base matrix comprises one of a non-negative integer and “−1”. 30.The method of claim 24, wherein the code rate is ⅔ and the first basematrix comprises: $\begin{bmatrix}2 & {- 1} & 19 & {- 1} & 47 & {- 1} & 48 & {- 1} & 36 & {- 1} & 82 & {- 1} & 47 & {- 1} & 15 & {- 1} & 95 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 69 & {- 1} & 88 & {- 1} & 33 & {- 1} & 3 & {- 1} & 16 & {- 1} & 37 & {- 1} & 40 & {- 1} & 48 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\10 & {- 1} & 86 & {- 1} & 62 & {- 1} & 28 & {- 1} & 85 & {- 1} & 16 & {- 1} & 34 & {- 1} & 73 & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 28 & {- 1} & 32 & {- 1} & 81 & {- 1} & 27 & {- 1} & 88 & {- 1} & 5 & {- 1} & 56 & {- 1} & 37 & {- 1} & {- 1} & {- 1} & 0 & {\quad 0} & {- 1} & {- 1} & {- 1} \\23 & {- 1} & 29 & {- 1} & 15 & {- 1} & 30 & {- 1} & 66 & {- 1} & 24 & {- 1} & 50 & {- 1} & 62 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} & {- 1} \\{- 1} & 30 & {- 1} & 65 & {- 1} & 54 & {- 1} & 14 & {- 1} & 0 & {- 1} & 30 & {- 1} & 74 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} \\32 & {- 1} & 0 & {- 1} & 15 & {- 1} & 56 & {- 1} & 85 & {- 1} & 5 & {- 1} & 6 & {- 1} & 52 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} \\{- 1} & 0 & {- 1} & 47 & {- 1} & 13 & {- 1} & 61 & {- 1} & 84 & {- 1} & 55 & {- 1} & 78 & {- 1} & 41 & 95 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0}\end{bmatrix}\quad$
 31. A method of providing a base matrix for encodingor decoding data at a specific code rate using low density parity check(LDPC) code for a specific codeword length, the method comprising:providing a first base matrix, the first base matrix associated with afirst codeword length for a specified code rate and each locationcomprising a value; and generating a second base matrix by altering thevalue corresponding to each of specific locations of the first basematrix, the second base matrix associated with a second codeword length,wherein altering comprises flooring the value corresponding to each ofthe specific locations according to a number of columns and rows in afirst permutation matrix and a number of columns and rows in a secondpermutation matrix.
 32. The method of claim 31 wherein altering isperformed using a function comprising the form:shift(z)=floor (shift(z _(max))z/z _(max)) wherein z_(max) is the numberof columns and rows in the first permutation matrix, z is the number ofcolumns and rows in the second permutation matrix, shift (z_(max)) isthe value corresponding to a specific location in the first base matrix,shift(z) the altered value corresponding to the specific location in thesecond base matrix, and floor (x) is a flooring function that denotesthe nearest integer from x toward negative infinity.
 33. The method ofclaim 32, wherein z_(max) is
 96. 34. The method of claim 31, whereineach of the specific locations is a location comprising a positiveinteger.
 35. The method of claim 31, wherein the first codeword lengthis a maximum codeword length.
 36. The method of claim 31, wherein thespecified code rate is one of ½, ⅔ and ¾.
 37. A method of encoding ordecoding data at ⅔ code rate using low density parity check (LDPC) code,the method comprising using a base matrix comprising: $\begin{bmatrix}2 & {- 1} & 19 & {- 1} & 47 & {- 1} & 48 & {- 1} & 36 & {- 1} & 82 & {- 1} & 47 & {- 1} & 15 & {- 1} & 95 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 69 & {- 1} & 88 & {- 1} & 33 & {- 1} & 3 & {- 1} & 16 & {- 1} & 37 & {- 1} & 40 & {- 1} & 48 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\10 & {- 1} & 86 & {- 1} & 62 & {- 1} & 28 & {- 1} & 85 & {- 1} & 16 & {- 1} & 34 & {- 1} & 73 & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 28 & {- 1} & 32 & {- 1} & 81 & {- 1} & 27 & {- 1} & 88 & {- 1} & 5 & {- 1} & 56 & {- 1} & 37 & {- 1} & {- 1} & {- 1} & 0 & {\quad 0} & {- 1} & {- 1} & {- 1} \\23 & {- 1} & 29 & {- 1} & 15 & {- 1} & 30 & {- 1} & 66 & {- 1} & 24 & {- 1} & 50 & {- 1} & 62 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} & {- 1} \\{- 1} & 30 & {- 1} & 65 & {- 1} & 54 & {- 1} & 14 & {- 1} & 0 & {- 1} & 30 & {- 1} & 74 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} \\32 & {- 1} & 0 & {- 1} & 15 & {- 1} & 56 & {- 1} & 85 & {- 1} & 5 & {- 1} & 6 & {- 1} & 52 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} \\{- 1} & 0 & {- 1} & 47 & {- 1} & 13 & {- 1} & 61 & {- 1} & 84 & {- 1} & 55 & {- 1} & 78 & {- 1} & 41 & 95 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0}\end{bmatrix}\quad$
 38. A method of decoding data using low densityparity check (LDPC) code, the method comprising: providing a permutationmatrix, a zero matrix and a base matrix; generating a parity matrix byexpanding the base matrix using the permutation matrix and zero matrix;and using the parity matrix to decode received data.
 39. The method ofclaim 38, wherein the base matrix is expanded by replacing a valuecorresponding to each of first specified locations in the base matrixwith one of the permutation matrix and an altered permutation matrixbased on the first permutation matrix, and replacing a valuecorresponding to each of second specified locations in the base matrixwith the zero matrix.
 40. The method of claim 39, wherein each of thefirst specified locations is a location comprising a non-negativeinteger and each of the second specified locations is a locationcomprising a negative integer.
 41. The method of claim 38, wherein eachlocation of the base matrix contains one of a non-negative integer and“−1” and expanding the base matrix comprises: replacing each location ofthe base matrix containing “−1” with the contents of the zero matrix;replacing each location of the base matrix containing a positive integerwith the permutation matrix altered according to the positive integer;and replacing each location of the base matrix containing a zero withthe first permutation matrix in an unaltered state.
 42. The method ofclaim 41, wherein the permutation matrix is altered by circular shiftingone of each entire row and each entire column a number of intervalsequal to the positive integer.
 43. The method of claim 38, wherein thenumber of columns and the number of rows of the permutation matrix arethe same and are equal to the number of columns and the number of rowsof the zero matrix.
 44. The method of claim 38, wherein the permutationmatrix is defined as having a row weight and column weight of “1”. 45.The method of claim 38, wherein the number of rows and the number ofcolumns in the permutation matrix is equal to z and the number of rowsof the base matrix is equal to the number of columns in the paritymatrix divided by z and multiplied by (1−(a coding rate)).
 46. Themethod of claim 38, further comprising: providing a first base matrix,the first base matrix associated with a first codeword length for aspecified code rate and each location comprising a value; and generatinga second base matrix by altering the value corresponding to each ofspecific locations of the first base matrix, the second base matrixassociated with a second codeword length, wherein altering comprisesflooring the value corresponding to each of the specific locationsaccording to a number of columns and rows in a first permutation matrixand a number of columns and rows in a second permutation matrix.
 47. Themethod of claim 46, wherein each of the specific locations is a locationcomprising a positive integer.
 48. The method of claim 46, whereinaltering is performed using a function comprising the form:shift(z)=floor (shift(z _(max))z/z _(max)) wherein z_(max) is the numberof columns and rows in the first permutation matrix, z is the number ofcolumns and rows in the second permutation matrix, shift (z_(max)) isthe value corresponding to a specific location in the first base matrix,shift(z) is an altered value corresponding to the specific location inthe second base matrix, and floor (x) is a flooring function thatdenotes the nearest integer from x toward negative infinity.
 49. Themethod of claim 48, wherein z_(max) is
 96. 50. The method of claim 46,wherein the first codeword length is a maximum codeword length.
 51. Themethod of claim 46, wherein the specified code rate is one of ½, ⅔ and¾.
 52. The method of claim 46, wherein each location of the base matrixcomprises one of a non-negative integer and “−1”.
 53. The method ofclaim 46, wherein the code rate is ⅔ and the first base matrixcomprises: $\begin{bmatrix}2 & {- 1} & 19 & {- 1} & 47 & {- 1} & 48 & {- 1} & 36 & {- 1} & 82 & {- 1} & 47 & {- 1} & 15 & {- 1} & 95 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 69 & {- 1} & 88 & {- 1} & 33 & {- 1} & 3 & {- 1} & 16 & {- 1} & 37 & {- 1} & 40 & {- 1} & 48 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\10 & {- 1} & 86 & {- 1} & 62 & {- 1} & 28 & {- 1} & 85 & {- 1} & 16 & {- 1} & 34 & {- 1} & 73 & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 28 & {- 1} & 32 & {- 1} & 81 & {- 1} & 27 & {- 1} & 88 & {- 1} & 5 & {- 1} & 56 & {- 1} & 37 & {- 1} & {- 1} & {- 1} & 0 & {\quad 0} & {- 1} & {- 1} & {- 1} \\23 & {- 1} & 29 & {- 1} & 15 & {- 1} & 30 & {- 1} & 66 & {- 1} & 24 & {- 1} & 50 & {- 1} & 62 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} & {- 1} \\{- 1} & 30 & {- 1} & 65 & {- 1} & 54 & {- 1} & 14 & {- 1} & 0 & {- 1} & 30 & {- 1} & 74 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} \\32 & {- 1} & 0 & {- 1} & 15 & {- 1} & 56 & {- 1} & 85 & {- 1} & 5 & {- 1} & 6 & {- 1} & 52 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} \\{- 1} & 0 & {- 1} & 47 & {- 1} & 13 & {- 1} & 61 & {- 1} & 84 & {- 1} & 55 & {- 1} & 78 & {- 1} & 41 & 95 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0}\end{bmatrix}\quad$
 54. An apparatus for encoding data using low densityparity check (LDPC) code, the apparatus comprising: a data sourceadapted to provide data to be transmitted; an LPDC encoder adapted togenerate a parity matrix by expanding the base matrix using apermutation matrix and a zero matrix and encode the data to betransmitted using the parity matrix; a modulation module adapted tomodulate the encoded data to generate modulated encoded data; and anantenna adapted to transmit the modulated encoded data.
 55. Theapparatus of claim 54, wherein the LPDC encoder is adapted to expand thebase matrix by replacing a value corresponding to each of firstspecified locations in the base matrix with one of the permutationmatrix and an altered permutation matrix based on the first permutationmatrix, and replace a value corresponding to each of second specifiedlocations in the base matrix with the zero matrix.
 56. The apparatus ofclaim 55, wherein each of the first specified locations is a locationcomprising a non-negative integer and each of the second specifiedlocations is a location comprising a negative integer.
 57. The apparatusof claim 55, wherein each location of the base matrix contains one of anon-negative integer and “−1” and the LPDC encoder is adapted to expandthe base matrix by: replacing each location of the base matrixcontaining “−1” with the contents of the zero matrix; replacing eachlocation of the base matrix containing a positive integer with thepermutation matrix altered according to the positive integer; andreplacing each location of the base matrix containing a zero with thepermutation matrix in an unaltered state.
 58. The apparatus of claim 57,wherein the LPDC encoder is adapted to alter the permutation matrix bycircular shifting one of each entire row and each entire column a numberof intervals equal to the positive integer.
 59. The apparatus of claim54, wherein the number of columns and the number of rows of thepermutation matrix are the same and are equal to the number of columnsand the number of rows of the zero matrix.
 60. The apparatus of claim54, wherein the permutation matrix is defined as having a row weight andcolumn weight of “1”.
 61. The apparatus of claim 54, wherein the numberof rows and columns in the permutation matrix is equal to z and thenumber of rows of the base matrix is equal to the number of columns inthe parity matrix divided by z and multiplied by (1−(a coding rate)).62. The apparatus of claim 54, wherein the LPDC encoder is furtheradapted to generate a second base matrix by altering a valuecorresponding to each of specific locations of a first base matrix, thefirst base matrix associated with a first codeword length for aspecified code rate and the second base matrix associated with a secondcodeword length, wherein altering comprises flooring the valuecorresponding to each of the specific locations according to a number ofcolumns and rows in a first permutation matrix and a number of columnsand rows in a second permutation matrix.
 63. The apparatus of claim 62,wherein the LPDC encoder is further adapted to alter the valuecorresponding to each of specific locations using a function comprisingthe form:shift(z)=floor (shift(z _(max))z/z _(max)) wherein z_(max) is the numberof columns and rows in the first permutation matrix, z is the number ofcolumns and rows in the second permutation matrix, shift (z_(max)) isthe value corresponding to a specific location in the first base matrix,shift(z) is an altered value corresponding to the specific location inthe second base matrix, and floor (x) is a flooring function thatdenotes the nearest integer from x toward negative infinity.
 64. Theapparatus of claim 63, wherein z_(max) is
 96. 65. The apparatus of claim62, wherein the LDPC encoder comprises: a memory module adapted to storeinformation related to the first base matrix, the first permutationmatrix and the second permutation matrix; a base matrix generationmodule adapted to generate the second base matrix by altering the valuecorresponding to each of specific locations of the first base matrixusing a flooring function; a parity matrix generation module adapted togenerate the parity matrix by expanding the second base matrix using thepermutation matrix and the zero matrix; and an encoding module adaptedto encode the data to be transmitted using the parity matrix.
 66. Theapparatus of claim 65, wherein the functions of at least one of the basematrix generation module, the parity matrix generation module and thedecoding module are implemented in software.
 67. The apparatus of claim65, wherein the functions of at least one of the base matrix generationmodule, the parity matrix generation module and the decoding module areimplemented in hardware.
 68. The apparatus of claim 62, wherein each ofthe specific locations is a location comprising a positive integer. 69.The apparatus of claim 62, wherein the first codeword length is amaximum codeword length.
 70. The apparatus of claim 62, wherein thespecified code rate is one of ½, ⅔ and ¾.
 71. The apparatus of claim 62,wherein each location of the base matrix comprises one of a non-negativeinteger and “−1”.
 72. The apparatus of claim 62, wherein the code rateis ⅔ and the first base matrix comprises: $\begin{bmatrix}2 & {- 1} & 19 & {- 1} & 47 & {- 1} & 48 & {- 1} & 36 & {- 1} & 82 & {- 1} & 47 & {- 1} & 15 & {- 1} & 95 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 69 & {- 1} & 88 & {- 1} & 33 & {- 1} & 3 & {- 1} & 16 & {- 1} & 37 & {- 1} & 40 & {- 1} & 48 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\10 & {- 1} & 86 & {- 1} & 62 & {- 1} & 28 & {- 1} & 85 & {- 1} & 16 & {- 1} & 34 & {- 1} & 73 & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 28 & {- 1} & 32 & {- 1} & 81 & {- 1} & 27 & {- 1} & 88 & {- 1} & 5 & {- 1} & 56 & {- 1} & 37 & {- 1} & {- 1} & {- 1} & 0 & {\quad 0} & {- 1} & {- 1} & {- 1} \\23 & {- 1} & 29 & {- 1} & 15 & {- 1} & 30 & {- 1} & 66 & {- 1} & 24 & {- 1} & 50 & {- 1} & 62 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} & {- 1} \\{- 1} & 30 & {- 1} & 65 & {- 1} & 54 & {- 1} & 14 & {- 1} & 0 & {- 1} & 30 & {- 1} & 74 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} \\32 & {- 1} & 0 & {- 1} & 15 & {- 1} & 56 & {- 1} & 85 & {- 1} & 5 & {- 1} & 6 & {- 1} & 52 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} \\{- 1} & 0 & {- 1} & 47 & {- 1} & 13 & {- 1} & 61 & {- 1} & 84 & {- 1} & 55 & {- 1} & 78 & {- 1} & 41 & 95 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0}\end{bmatrix}\quad$
 73. An apparatus for decoding data using low densityparity check (LDPC) code, the apparatus comprising: an antenna adaptedto receive modulated encoded data; a demodulation module adapted todemodulate the modulated encoded data to generate encoded data; and anLPDC decoder adapted to generate a parity matrix by expanding the basematrix using a permutation matrix and a zero matrix and decode theencoded data using the parity matrix;
 74. The apparatus of claim 73,wherein the LPDC encoder is adapted to expand the base matrix byreplacing a value corresponding to each of first specified locations inthe base matrix with one of the permutation matrix and an alteredpermutation matrix based on the first permutation matrix, and replace avalue corresponding to each of second specified locations in the basematrix with the zero matrix.
 75. The apparatus of claim 74, wherein eachof the first specified locations is a location comprising a non-negativeinteger and each of the second specified locations is a locationcomprising a negative integer.
 76. The apparatus of claim 74, whereineach location of the base matrix contains one of a non-negative integerand “−1” and the LPDC encoder is adapted to expand the base matrix by:replacing each location of the base matrix containing “−1” with thecontents of the zero matrix; replacing each location of the base matrixcontaining a positive integer with the permutation matrix alteredaccording to the positive integer; and replacing each location of thebase matrix containing a zero with the permutation matrix in anunaltered state.
 77. The apparatus of claim 76, wherein the LPDC encoderis adapted to alter the permutation matrix by circular shifting one ofeach entire row and each entire column a number of intervals equal tothe positive integer.
 78. The apparatus of claim 73, wherein the numberof columns and the number of rows of the permutation matrix are the sameand are equal to the number of columns and the number of rows of thezero matrix.
 79. The apparatus of claim 73, wherein the permutationmatrix is defined as having a row weight and column weight of “1”. 80.The apparatus of claim 73, wherein the number of rows and columns in thepermutation matrix is equal to z and the number of rows of the basematrix is equal to the number of columns in the parity matrix divided byz and multiplied by (1−(a coding rate)).
 81. The apparatus of claim 73,wherein the LPDC encoder is further adapted to generate a second basematrix by altering a value corresponding to each of specific locationsof a first base matrix, the first base matrix associated with a firstcodeword length for a specified code rate and the second base matrixassociated with a second codeword length, wherein altering comprisesflooring the value corresponding to each of the specific locationsaccording to a number of columns and rows in a first permutation matrixand a number of columns and rows in a second permutation matrix.
 82. Theapparatus of claim 81, wherein the LPDC encoder is further adapted toalter the value corresponding to each of specific locations using afunction comprising the form:shift(z)=floor (shift(z _(max))z/z _(max)) wherein z_(max) is the numberof columns and rows in the first permutation matrix, z is the number ofcolumns and rows in the second permutation matrix, shift (z_(max)) isthe value corresponding to a specific location in the first base matrix,shift(z) is an altered value corresponding to the specific location inthe second base matrix, and floor (x) is a flooring function thatdenotes the nearest integer from x toward negative infinity.
 83. Theapparatus of claim 82, wherein z_(max) is
 96. 84. The apparatus of claim81, wherein the LDPC encoder comprises: a memory module adapted to storeinformation related to the first base matrix, the first permutationmatrix and the second permutation matrix; a base matrix generationmodule adapted to generate the second base matrix by altering the valuecorresponding to each of specific locations of the first base matrixusing a flooring function; a parity matrix generation module adapted togenerate the parity matrix by expanding the second base matrix using thepermutation matrix and the zero matrix; and an decoding module adaptedto decode the encoded data using the parity matrix.
 85. The apparatus ofclaim 84, wherein the functions of at least one of the base matrixgeneration module, the parity matrix generation module and the decodingmodule are implemented in software.
 86. The apparatus of claim 84,wherein the functions of at least one of the base matrix generationmodule, the parity matrix generation module and the decoding module areimplemented in hardware.
 87. The apparatus of claim 81, wherein each ofthe specific locations is a location comprising a positive integer. 88.The apparatus of claim 81, wherein the first codeword length is amaximum codeword length.
 89. The apparatus of claim 81, wherein thespecified code rate is one of ½, ⅔ and ¾.
 90. The apparatus of claim 81,wherein each location of the base matrix comprises one of a non-negativeinteger and “−1”.
 91. The apparatus of claim 81, wherein the code rateis ⅔ and the first base matrix comprises: $\begin{bmatrix}2 & {- 1} & 19 & {- 1} & 47 & {- 1} & 48 & {- 1} & 36 & {- 1} & 82 & {- 1} & 47 & {- 1} & 15 & {- 1} & 95 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 69 & {- 1} & 88 & {- 1} & 33 & {- 1} & 3 & {- 1} & 16 & {- 1} & 37 & {- 1} & 40 & {- 1} & 48 & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\10 & {- 1} & 86 & {- 1} & 62 & {- 1} & 28 & {- 1} & 85 & {- 1} & 16 & {- 1} & 34 & {- 1} & 73 & {- 1} & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 28 & {- 1} & 32 & {- 1} & 81 & {- 1} & 27 & {- 1} & 88 & {- 1} & 5 & {- 1} & 56 & {- 1} & 37 & {- 1} & {- 1} & {- 1} & 0 & {\quad 0} & {- 1} & {- 1} & {- 1} \\23 & {- 1} & 29 & {- 1} & 15 & {- 1} & 30 & {- 1} & 66 & {- 1} & 24 & {- 1} & 50 & {- 1} & 62 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} & {- 1} \\{- 1} & 30 & {- 1} & 65 & {- 1} & 54 & {- 1} & 14 & {- 1} & 0 & {- 1} & 30 & {- 1} & 74 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} & {- 1} \\32 & {- 1} & 0 & {- 1} & 15 & {- 1} & 56 & {- 1} & 85 & {- 1} & 5 & {- 1} & 6 & {- 1} & 52 & {- 1} & 0 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0} & {\quad 0} \\{- 1} & 0 & {- 1} & 47 & {- 1} & 13 & {- 1} & 61 & {- 1} & 84 & {- 1} & 55 & {- 1} & 78 & {- 1} & 41 & 95 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & {\quad 0}\end{bmatrix}\quad$